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rudyjanay

A grain silo is shown below. What is the volume of grain that could completely fill this silo rounded to the nearest whole number? Use 22/7 for pi. 19,008 ft3 19,461 ft3 6,336 ft3 453 ft3

  • one year ago
  • one year ago

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  1. rudyjanay
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    • one year ago
  2. agentx5
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    Sum together half of a sphere for the top part, with a cylinder for the bottom part. That's all there is to it :-) Do you know the formulas for a cylinder and a sphere? h = 168 ft r = 6 ft

    • one year ago
  3. rudyjanay
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    no i don't

    • one year ago
  4. agentx5
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    \[\large V_{sphere} = \frac{4 \pi r ^3}{3}\] \[\large V_{cylinder} = \pi r^2 h\] \[V_{total} = \frac{V_{sphere}}{2} + V_{cylinder}\]

    • one year ago
  5. agentx5
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    Can you solve it now? ;-D

    • one year ago
  6. rudyjanay
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    no i'm sorry i'm completely lost :-(

    • one year ago
  7. agentx5
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    r = radius (both for the cylinder and sphere) , h = height of the cylinder Separate the curved, hemispherical top from the cylinder under it. You'll just add volume the two shapes together. What are you confused on specifically?

    • one year ago
  8. rudyjanay
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    i'm just naturally confused on everything that has to do with maths you have to talk to me like a toddler and tell mi step by step

    • one year ago
  9. agentx5
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    Can you identify the radius in the drawing? And the height?

    • one year ago
  10. rudyjanay
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    the radius for the entire drawing?

    • one year ago
  11. agentx5
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    There's only one radius, yes. It works for both the sphere and cylinder, like I said.

    • one year ago
  12. rudyjanay
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    is it 6 ft?

    • one year ago
  13. agentx5
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    Yes... |dw:1342123496209:dw|

    • one year ago
  14. agentx5
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    And height is "h", which is?

    • one year ago
  15. rudyjanay
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    168 ft

    • one year ago
  16. abhishekjha29
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    2/3*22/7*6*6*6 + 1/3*@22/7*6*6*168 = ............

    • one year ago
  17. agentx5
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    Ok, now scroll up and put r & h into those two equations for the Volume of a Sphere and Cylinder. Substitute, replacing r with "(6 ft)", and replacing h with "(168 ft)".

    • one year ago
  18. rudyjanay
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    ok

    • one year ago
  19. abhishekjha29
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    |dw:1342123834485:dw| find the volume of given figure

    • one year ago
  20. agentx5
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    @abhishekjha29 no, it's a cylinder under a hemisphere, not a cone.

    • one year ago
  21. abhishekjha29
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    ya tats ok.but i have a new figure wid a cone instead of culinder

    • one year ago
  22. rudyjanay
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    so i use 3/4 3.14 times 6 to the 3rd power to find the volume of the sphere?

    • one year ago
  23. agentx5
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    ??? @abhishekjha29 the volume of a cone = \(\large\frac{\pi r ^2 h}{3}\) , exactly a third of a cylinder's volume with the same dimensions for height and radius.

    • one year ago
  24. rudyjanay
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    oh ok

    • one year ago
  25. rudyjanay
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    when i do it it tells me that the volume for the cylinder is 6330.24

    • one year ago
  26. agentx5
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    @rudyjanay I would leave the 3.1415... \(\pi\) out of it until the end, just keep it along like it's a unit like "feet". You can indeed do that above, but keep in mind it will be an estimate because: \(\pi \approx 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 062...\)

    • one year ago
  27. agentx5
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    Best to just leave it alone until you're all done with the formulas :-D

    • one year ago
  28. agentx5
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    Kind of like how I did in the cylinder part above, if you see what I did

    • one year ago
  29. agentx5
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    When you're all done, multiply that big, non-decimal number and it'll give you your messy decimal answer.

    • one year ago
  30. rudyjanay
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    ok i'll try leaving the 3.14 out

    • one year ago
  31. agentx5
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    :-) I think you've got it down now It's just plug & chug once you got the setup up done. The tricky part was recognizing it's half of a sphere (a hemisphere) plus a cylinder added together, and that the cylinder and the hemisphere have the same radius.

    • one year ago
  32. rudyjanay
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    oh i guess my phone was giving me the wrong answer because i don't have a calculator with me

    • one year ago
  33. rudyjanay
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    the answer that i got is 19 461

    • one year ago
  34. agentx5
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    I just noticed I made a typo let me correct myself... \[\large V_{cylinder} = \pi r^2 h\] \[\large V_{cylinder} = \pi (6 \ ft)^2 (168 \ ft)\] \[\large V_{cylinder} = \pi (36 \ ft^2)(168 \ ft)\] \[\large V_{cylinder} = 6048\pi \ ft^3\] And back into the total... \[\large V_{total} = \frac{288\pi \ ft^3}{2} + (6048\pi ft^3)\] \[\large V_{total} = 144\pi \ ft^3 + 6048\pi ft^3\] \[\large V_{total} = 6192\pi \ ft^3 \approx \ 19452.74171... ft^3\]

    • one year ago
  35. rudyjanay
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    oh so i was right

    • one year ago
  36. agentx5
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    So yes, you're good. The answer choice you were given is actually an estimate, and not as exact as what I just did :-)

    • one year ago
  37. rudyjanay
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    ohhhh great thank you

    • one year ago
  38. agentx5
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    6292\(\pi\) ft\(^3\) is the exact answer, and what I would be expect to do at work

    • one year ago
  39. agentx5
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    Because if a construction firm wants to make an estimate to their liking, they can just pull out their pocket calculator or smartphone and see how many decimal places they care about for the project

    • one year ago
  40. agentx5
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    Sometimes accuracy is critical and a matter of life & death, other times you don't have to be so particular

    • one year ago
  41. rudyjanay
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    thats why i don't get maths

    • one year ago
  42. agentx5
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    Example of where accuracy is a matter of life & death: ammunition factory. Even the smallest screw up could mean a detonation, a dud bullet in a critical field operation that means some cop or soldier gets killed, contracts being canceled etc. Another good example would be a factory where they make care engines. If they get the radius slightly wrong your engine won't work well or is more prone to breakdowns. Math can seem useless until you have something that makes it mean something :-)

    • one year ago
  43. agentx5
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    Car engines* lol not "care"

    • one year ago
  44. rudyjanay
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    are you a math wiz or something

    • one year ago
  45. agentx5
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    Engineering student. I'm not mathematician, but I love the application of it to stuff that matters :-3 Fire & explosives for example is a specialty of mine, and game design is my hobby (which also uses math quiet a bit because of physics stuff).

    • one year ago
  46. agentx5
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    Math itself though, meh... I loose focus if it doesn't mean anything practical.

    • one year ago
  47. rudyjanay
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    oh ok i'm gonna check on my other question

    • one year ago
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